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Optimal Consumption And Portfolio Selection With Incomplete Markets And Upper And Lower Bound Constraints

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  • Hiroshi Shirakawa

Abstract

We study an optimal consumption and portfolio selection problem for an investor by a martingale approach. We assume that time is a discrete and finite horizon, the sample space is finite and the number of securities is smaller than that of the possible securities price vector transitions. the investor is prohibited from investing stocks more (less, respectively) than given upper (lower) bounds at any time, and he maximizes an expected time additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. Also we state the existence of the unique primal optimal solutions. Next we formulate a dual control problem and establish the duality between primal and dual control problems. Also we show the existence of dual optimal solutions. Finally we consider the computational aspect of dual approach through a simple numerical example.

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  • Hiroshi Shirakawa, 1994. "Optimal Consumption And Portfolio Selection With Incomplete Markets And Upper And Lower Bound Constraints," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 1-24, January.
    • Handle: RePEc:bla:mathfi:v:4:y:1994:i:1:p:1-24
    DOI: 10.1111/j.1467-9965.1994.tb00047.x
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    Cited by:

    1. Bardhan, Indrajit, 1995. "Synthetic replication of American contingent claims when portfolios are constrained," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 149-165, May.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Wenyuan Wang & Kaixin Yan & Xiang Yu, 2023. "Optimal Portfolio with Ratio Type Periodic Evaluation under Short-Selling Prohibition," Papers 2311.12517, arXiv.org, revised Dec 2023.

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